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South Korean IMO Shortlist 2010 Inequality

Source: IMO Shortlist 2010, Algebra 8

July 17, 2011
inequalitiesalgebraIMO Shortlist

Problem Statement

Given six positive numbers a,b,c,d,e,fa,b,c,d,e,f such that a<b<c<d<e<f.a < b < c < d < e < f. Let a+c+e=Sa+c+e=S and b+d+f=T.b+d+f=T. Prove that 2ST>3(S+T)(S(bd+bf+df)+T(ac+ae+ce)).2ST > \sqrt{3(S+T)\left(S(bd + bf + df) + T(ac + ae + ce) \right)}.
Proposed by Sung Yun Kim, South Korea
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